{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OKF22ONWBBWS3F6QJEIPSA7DL7","short_pith_number":"pith:OKF22ONW","schema_version":"1.0","canonical_sha256":"728bad39b6086d2d97d04910f903e35fe300aa8259966959b6b1743eeb782a1b","source":{"kind":"arxiv","id":"1708.04723","version":1},"attestation_state":"computed","paper":{"title":"Polylogarithmic approximation for minimum planarization (almost)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anastasios Sidiropoulos, Ken-ichi Kawarabayashi","submitted_at":"2017-08-15T23:54:36Z","abstract_excerpt":"In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a $\\log^{O(1)} n$-approximation algorithm for this problem on general graphs with running time $n^{O(\\log n/\\log\\log n)}$. We also obtain a $O(n^\\varepsilon)$-approximation with running time $n^{O(1/\\varepsilon)}$ for any arbitrarily small constant $\\varepsilon > 0$. Prior to our work, no non-trivial algorithm was known for this problem on general graphs, and the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.04723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-08-15T23:54:36Z","cross_cats_sorted":[],"title_canon_sha256":"5c37dfc69657bacdaf363c3541cc77dea42212d612300e9578cbcf0721047fc4","abstract_canon_sha256":"cfe68cfe649e497cdc6ecb2c8bf93213a74bc088d896b75b43fd236fc7dfbff2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:58.086956Z","signature_b64":"j7LaJZRrISTk3ofP5WbM608Lvgtirfo/seg0UAokSFjVycC6auAmsu1dicwqCfUd0Vw31gOYijO54NJ3Na/fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"728bad39b6086d2d97d04910f903e35fe300aa8259966959b6b1743eeb782a1b","last_reissued_at":"2026-05-18T00:37:58.086294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:58.086294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polylogarithmic approximation for minimum planarization (almost)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anastasios Sidiropoulos, Ken-ichi Kawarabayashi","submitted_at":"2017-08-15T23:54:36Z","abstract_excerpt":"In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a $\\log^{O(1)} n$-approximation algorithm for this problem on general graphs with running time $n^{O(\\log n/\\log\\log n)}$. We also obtain a $O(n^\\varepsilon)$-approximation with running time $n^{O(1/\\varepsilon)}$ for any arbitrarily small constant $\\varepsilon > 0$. Prior to our work, no non-trivial algorithm was known for this problem on general graphs, and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04723","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.04723","created_at":"2026-05-18T00:37:58.086425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04723v1","created_at":"2026-05-18T00:37:58.086425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04723","created_at":"2026-05-18T00:37:58.086425+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKF22ONWBBWS","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKF22ONWBBWS3F6Q","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKF22ONW","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7","json":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7.json","graph_json":"https://pith.science/api/pith-number/OKF22ONWBBWS3F6QJEIPSA7DL7/graph.json","events_json":"https://pith.science/api/pith-number/OKF22ONWBBWS3F6QJEIPSA7DL7/events.json","paper":"https://pith.science/paper/OKF22ONW"},"agent_actions":{"view_html":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7","download_json":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7.json","view_paper":"https://pith.science/paper/OKF22ONW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04723&json=true","fetch_graph":"https://pith.science/api/pith-number/OKF22ONWBBWS3F6QJEIPSA7DL7/graph.json","fetch_events":"https://pith.science/api/pith-number/OKF22ONWBBWS3F6QJEIPSA7DL7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7/action/storage_attestation","attest_author":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7/action/author_attestation","sign_citation":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7/action/citation_signature","submit_replication":"https://pith.science/pith/OKF22ONWBBWS3F6QJEIPSA7DL7/action/replication_record"}},"created_at":"2026-05-18T00:37:58.086425+00:00","updated_at":"2026-05-18T00:37:58.086425+00:00"}